Since hearing about Parrondo’s Paradox (referred to as PP from here on in) and seeing the attempts at making it work for trading I decided to check it out. SMJones appears to have come up with an EA that implements PP in his thread titled Modified Parrondo’s Paradox but without also testing the individual games alongside the paradox then the test is actually incomplete. I know this because you can still use PP and make positive returns because it will at worst average the three games (ie a positive return for a PP system does not mean the other games are individually worse – its more likely that some of them are better).

I decided to create a simple and quick MS Access application (which I will post here later on) that runs the Original and Coop Parrondo’s Paradox simulations to whatever setting you would like to give them. I did create a Excel version but I wasn’t happy with it (mainly because the performance was crap). I haven’t created a proper .NET version because unfortunately I don’t see its worth – yet.

Over the next days I will run numerous tests using my app and post the results and graphs so I can show those of you who have PM’ed me questions regarding PP and also those who are thinking of trying to create an EA with it.

To kick things off I will explain how the simulator works - and this is the Original PP for the time being.

Spread: this is set to 1 pip

Cycles: these are the number of cycles to run in one go before resetting some of tracking variables (including the randomiser)

Iterations: these are the number of complete cycles to run.

Mod: 3 (set at 3 for the classic Original PP but it can be anything from 2 to whatever)

There are 3 games, named A, B1 and B2. Each game has its own:

-Win and Loss amounts in pips (in both pre-spread and post spread)

-Win and Loss amounts in steps (defaults to 1 – this is self explanatory in the sim test).

-Probability

-Edge. The edge gives each game its own um edge.

Please seek other sources for more depth regarding the games.

The simulator outputs all the cycle and iteration results to a table (for study purposes) and also outputs three different charts. Chart 1 shows only the “step” results for all of the following five games and combinations whilst Chart 2 shows the pip results for these:

1)PP

2)Game A only

3)Game B only (B1 and B2 combined using same mod rules as the PP)

4)Game B1 only

5)Game B2 only

Chart 3 only shows the step results for PP, Game A and Game B (namely for clarity purposes because game B2 is always sky rocketing)

Because I am using VBA’s semi-broken random number generator I have included several controls to monitor the actually randomness of the values used.

Important things to note:

1)Games B1 and B2 must be “fair” or PP does not work. The formula for making B1 and B2 fair is:

Prob(B2) = (1 - Prob(B1) - Sqr(Prob(B1) - (Prob(B1) * Prob(B1)))) / (1 - (2 *Prob(B1)))

2)The making and breaking of using PP for trading is the tracking of the Steps and Pips individually. The classic coin toss is equivalent to the steps and pips being the same, ie 1 for win, -1 for a loss. This is not suitable for trading.

Comments:

Something to keep in mind regarding PP. By definition the original PP was discovered to show two losing games (Game A and Game B – which is game B1 and B2 together) could be combined together to create an overall winning strategy. And that’s it. As far as I can see this will not work in trading because there will always be a Game (mostly B2) that will always perform better than the PP. I think the trick is to see if rules of PP can be bent such a combination of Games will make the performance of PP much better than any of the individual games. So far, in my opinion, PP will not work for trading but I have achieved some interesting results using parameters very different to the original PP’s parameters

Overall that’s about it, I will be updating this daily with new sim results and some explanations etc.

Here is a sample of Chart’s 1 and 2:

Quite clearly you can see the yellow PP line which positive gains in the Step chart (Chart 1) but it loses in the pips chart (Chart 2)

More later …

http://i573.photobucket.com/albums/s...ep_090727A.jpg

http://i573.photobucket.com/albums/s...ps_090727A.jpg

I decided to create a simple and quick MS Access application (which I will post here later on) that runs the Original and Coop Parrondo’s Paradox simulations to whatever setting you would like to give them. I did create a Excel version but I wasn’t happy with it (mainly because the performance was crap). I haven’t created a proper .NET version because unfortunately I don’t see its worth – yet.

Over the next days I will run numerous tests using my app and post the results and graphs so I can show those of you who have PM’ed me questions regarding PP and also those who are thinking of trying to create an EA with it.

To kick things off I will explain how the simulator works - and this is the Original PP for the time being.

__Firstly the overall parameters:__Spread: this is set to 1 pip

Cycles: these are the number of cycles to run in one go before resetting some of tracking variables (including the randomiser)

Iterations: these are the number of complete cycles to run.

Mod: 3 (set at 3 for the classic Original PP but it can be anything from 2 to whatever)

__Game Parameters:__There are 3 games, named A, B1 and B2. Each game has its own:

-Win and Loss amounts in pips (in both pre-spread and post spread)

-Win and Loss amounts in steps (defaults to 1 – this is self explanatory in the sim test).

-Probability

-Edge. The edge gives each game its own um edge.

Please seek other sources for more depth regarding the games.

__The Outputs__The simulator outputs all the cycle and iteration results to a table (for study purposes) and also outputs three different charts. Chart 1 shows only the “step” results for all of the following five games and combinations whilst Chart 2 shows the pip results for these:

1)PP

2)Game A only

3)Game B only (B1 and B2 combined using same mod rules as the PP)

4)Game B1 only

5)Game B2 only

Chart 3 only shows the step results for PP, Game A and Game B (namely for clarity purposes because game B2 is always sky rocketing)

Because I am using VBA’s semi-broken random number generator I have included several controls to monitor the actually randomness of the values used.

Important things to note:

1)Games B1 and B2 must be “fair” or PP does not work. The formula for making B1 and B2 fair is:

Prob(B2) = (1 - Prob(B1) - Sqr(Prob(B1) - (Prob(B1) * Prob(B1)))) / (1 - (2 *Prob(B1)))

2)The making and breaking of using PP for trading is the tracking of the Steps and Pips individually. The classic coin toss is equivalent to the steps and pips being the same, ie 1 for win, -1 for a loss. This is not suitable for trading.

Comments:

Something to keep in mind regarding PP. By definition the original PP was discovered to show two losing games (Game A and Game B – which is game B1 and B2 together) could be combined together to create an overall winning strategy. And that’s it. As far as I can see this will not work in trading because there will always be a Game (mostly B2) that will always perform better than the PP. I think the trick is to see if rules of PP can be bent such a combination of Games will make the performance of PP much better than any of the individual games. So far, in my opinion, PP will not work for trading but I have achieved some interesting results using parameters very different to the original PP’s parameters

Overall that’s about it, I will be updating this daily with new sim results and some explanations etc.

Here is a sample of Chart’s 1 and 2:

Quite clearly you can see the yellow PP line which positive gains in the Step chart (Chart 1) but it loses in the pips chart (Chart 2)

More later …

http://i573.photobucket.com/albums/s...ep_090727A.jpg

http://i573.photobucket.com/albums/s...ps_090727A.jpg